Invariant mode shape solutions of Kirchhoff uniform rectangular plates - Nunes, Afonso Willian [UNESP]; Silva, Samuel da [UNESP]; Dimas, Stylianos (My University, 2023)
The present work derives exact --- invariant --- solutions to the mode shape equation of uniform rectangular Kirchhoff plates via enhanced group analysis techniques. The study of the optimal system of the finite-dimensional Lie algebra of the admitted classical Lie point symmetries yields three nonequivalent invariant solutions to the studied equation. An additional invariant solution arises from nonclassical Lie point symmetries.
Keywords: Exact invariant solutions; Mode shape equation; Kirchhoff plate model; Enhanced group analysis; Lie point symmetries